Answer:
P(A∪B) = 1/3
Step-by-step explanation:
Red Garments = 1 red shirt + 1 red hat + 1 red pairs of pants
Total Red Garments = 3
Green Garments = 1 green shirt + 1 green scarf + 1 green pairs of pants
Total Green Garments = 3
The total number of garments = Total Red Garments + Total Green Garments:
3 + 3 = 6
Let A be the event that he selects a green garment
P(A) = Number of required outcomes/Total number of possible outcomes
P(A) = 3/6
Let B be the event that he chooses a scarf
P(B) = 1/6
The objective here is to determine P(A or B) = P(A∪B)
Using the probability set notation theory:
P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∩B) = Probability that a green pair of pant is chosen = P(A) - P(B)
= 3/6-1/6
= 2/6
P(A∪B) = 1/2 + 1/6 - 2/6
P(A∪B) = 2/6
P(A∪B) = 1/3
The lines y = 2x - 1 and y = -2x + 3 intersect at exactly one point which means this system has exactly one solution. so the system is consistent and independent
Answer:
b = 9.1units
Step-by-step explanation:
Find the diagram attached
Using the similarity theorem of triangle
WX/XZ = WY/WX
Substitute;
b/a+5 = 6/b
b² = 6(a+5) ... 1
Also according to pythagoras theorem on triangle WYX;
b² = 6²+a²...2
Equate 1 and 2
6(a+5) = 6²+a²
6a+30 = 36 + a²
a²-6a+36-30 = 0
a²-6a+6 = 0
a = 6±√36+4(6)/2
a = 6±√60/2
a = 6±7.745/2
a = 13.745/2
a = 6.8725
Recall that
b² = 6²+a²
b² = 36+6.8725²
b² = 83.2313
b = 9.12units
b = 9.1units
